Open AccessLegendre wavelet operational matrix method for solving fractional differential equations in some special conditions
Author(s) -
Aydın Seçer,
Selvi Altun,
Mustafa Bayram
Publication year - 2019
Publication title -
thermal science/thermal science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.339
H-Index - 43
eISSN - 2334-7163
pISSN - 0354-9836
DOI - 10.2298/tsci180920034s
Subject(s) - legendre wavelet , legendre polynomials , algebraic equation , associated legendre polynomials , mathematics , wavelet , legendre's equation , boundary value problem , fractional calculus , matrix (chemical analysis) , differential equation , mathematical analysis , orthogonal polynomials , computer science , wavelet transform , classical orthogonal polynomials , gegenbauer polynomials , discrete wavelet transform , nonlinear system , physics , materials science , artificial intelligence , composite material , quantum mechanics
This paper proposes a new technique which rests upon Legendre wavelets for solving linear and non-linear forms of fractional order initial and boundary value problems. In some particular circumstances, a new operational matrix of fractional derivative is generated by utilizing some significant properties of wavelets and orthogonal polynomials. We approached the solution in a finite series with respect to Legendre wavelets and then by using these operational matrices, we reduced the fractional differential equations into a system of algebraic equations. Finally, the introduced technique is tested on several illustrative examples. The obtained results demonstrate that this technique is a very impressive and applicable mathematical tool for solving fractional differential equations.